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  • Need solution for RD Sharma maths class 12 chapter 26 Direction Cosines and Direction Ratios exercise Fill in the blanks question 3

Need solution for RD Sharma maths class 12 chapter 26 Direction Cosines and Direction Ratios exercise Fill in the blanks question 3

Answers (1)

Final Answer : (l, m, n)=\left(0,-\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}\right)

 

Hint:

Direction cosine is cosine of angle made with the axes

 

Given:

\alpha=\frac{\pi}{2}, \beta=\frac{3 \pi}{4} \text { and } \gamma=\frac{\pi}{4}  are the angles made with x,y,z  axes.

To Find: 

Direction cosine of the line

Solution:

l=\cos \alpha, \quad m=\cos \beta, \quad n=\cos \gamma
\begin{aligned} &l=\cos \frac{\pi}{2}, \quad m=\cos \frac{3 \pi}{4}, \quad n=\cos \frac{\pi}{4} \\ &l=0, \quad m=-\frac{1}{\sqrt{2}}, \quad n=\frac{1}{\sqrt{2}} \end{aligned}

Therefore, the direction cosine of the line are   (l, m, x)=\left(0,-\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}\right)

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